IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 7, JULY 2011
779
Ant Colony Optimization Based Energy Saving Routing for Energy-Efficient Networks Young-Min Kim, Student Member, IEEE, Eun-Jung Lee, and Hong-Shik Park, Member, IEEE
Abstract—This letter proposes an ant colony optimization (ACO) based energy saving routing, referred to as A-ESR, for energy efficient networks. The proposed A-ESR algorithm firstly re-formulates the energy-consumption minimized network (EMN) problem, which is NP-complete, into a simpler one by using the concept of traffic centrality. After that, it solves the re-formulated problem by 1) letting the flow to autonomously be aggregated on some specific heavy-loaded links and 2) switching off the other light-loaded links. Simulation results show that the A-ESR algorithm can get better performance than previous works in terms of energy efficiency. Index Terms—Ant colony optimization, energy saving routing, A-ESR, traffic centrality, pheromone trails.
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I. I NTRODUCTION
ECENTLY, energy saving becomes a key issue in communication networks because energy consumption of the Internet is remarkably high and this consumption may exponentially grow as the Internet expands [1], [2]. However, as indicated in [3], network elements such as router and switch in current networks are not optimized for energy saving: they tend to consume the maximum energy although the carried traffic occupies only a small portion of their capacity, and their capacity is usually over-provisioned for accommodating future growth. Experiments in [2] mention this energy inefficiency of current network elements: there is little or no difference of energy consumption between peak and off-peak periods. To cope with this inefficiency, two types of approaches, classified as system-level and network-level, have been proposed. The system-level approaches [2], [3] are based on the following observation: if network elements can estimate idle periods of their outgoing links, they could reduce the energy consumption by switching off their relevant interfaces during the estimated idle periods. However, they intrinsically require redesign or replacement of the existing network elements to be capable of estimating the idle periods. The network-level approaches [4], [5] take a little different method: rather than developing intelligent network elements, they try to minimize the active network elements while still guaranteeing network connectivity. The authors in [4] formulate an integer linear programming (ILP) of the above problem, and propose some methods as its solutions. Although these methods can reduce the energy consumption quite effectively, solving the ILP problem is unfortunately not viable in large
Manuscript received April 26, 2011. The associate editor coordinating the review of this letter and approving it for publication was F. Granelli. This research was supported by the MKE, Korea, under the ITRC support program supervised by the NIPA (NIPA-2011-(C1090-1111-0013)) and the IT R&D program of MKE/KEIT (KI001810039160). The authors are with the Korea Advanced Institute of Science and Technology (KAIST), S. Korea (e-mail: injesus, freakone,
[email protected]). Digital Object Identifier 10.1109/LCOMM.2011.060811.110881
networks because it falls into the class of multi-commodity flow problems (i.e., NP-complete). The GreenOSPF algorithm in [5] slightly modifies the existing OSPF protocol (so, it is easy to implement) to share the shortest path tree of a specific node with neighbors of the node, and then solves the above problem by switching off the network elements which are excluded by the shared shortest paths. It, however, may waste energy under the highly dynamic network conditions because it only considers the topological information without knowledge of network state such as traffic demand. In this letter, we propose a novel network-level approach referred to as A-ESR for energy efficient networks. The proposed A-ESR algorithm exploits the ant colony optimization (ACO) method, which has been considered as a promising technique in solving combinatorial optimization problems [6]. Accordingly, due to the inheritance of swarm intelligence of artificial ants [7], compared with previous works, the A-ESR algorithm is adaptive to the highly varying network conditions. II. P ROBLEM D EFINITIONS Firstly we define the traffic centrality of a node as below. Definition (Traffic Centrality). If 𝑡𝑖𝑗 is a measure of traffic volume in bytes on link 𝑙𝑖𝑗 connecting node 𝑖 to its neighbor 𝑗, then the traffic centrality of node 𝑖 is defined as: 𝐶𝑘 (𝑖) = ∑
𝑡𝑖𝑘 𝑗∈𝑁𝑖 𝑡𝑖𝑗
,
where 𝑡𝑖𝑘 = max𝑗∈𝑁𝑖 𝑡𝑖𝑗 and 𝑁𝑖 is the set of neighbors of node 𝑖. 𝐶𝑘 (𝑖) (≤ 1) evaluates how densely carried traffic of node 𝑖 concentrates on a specific link 𝑙𝑖𝑘 . It is assumed that all links in the network have the same transmission capacity, and the same energy consumption profile. Corollary 1. As 𝐶𝑘 (𝑖) → 1 (i.e., maximizes), the energy consumption of node 𝑖 and its adjacent links can be minimized. ∑ Proof: To be 𝐶𝑘 (𝑖) → 1, 𝑡𝑖𝑘 ≈ 𝑗∈𝑁𝑖 𝑡𝑖𝑗 should be satisfied. It implies that 𝑡𝑖𝑗 (𝑗 ∈ 𝑁𝑖 , 𝑗 ∕= 𝑘) → 0 holds; that is, there exists little traffic on links 𝑙𝑖𝑗 (∕= 𝑙𝑖𝑘 ). Accordingly, node 𝑖 can minimize the energy consumption by forcing the carried traffic on 𝑙𝑖𝑗 (∕= 𝑙𝑖𝑘 ) to concentrate on link 𝑙𝑖𝑘 first, and then switching off 𝑙𝑖𝑗 (∕= 𝑙𝑖𝑘 ). By using the traffic centrality, we formulate an energy consumption-minimized network problem. Let 𝐺 = (𝑉, 𝐿) be a directed graph, where 𝑉 and 𝐿 are the set of nodes and links, respectively. Each node 𝑖 ∈ 𝑉 and link 𝑙 ∈ 𝐿 are characterized by the energy consumption functions 𝑒𝑣 (𝑖) : 𝑉 → 𝑅+ and 𝑒𝑙 (𝑙) : 𝐿 → 𝑅+ , respectively. Then, the energy consumptionminimized network (EMN) problem to be solved is defined:
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780
IEEE COMMUNICATIONS LETTERS, VOL. 15, NO. 7, JULY 2011
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node along the path and 𝑡𝑘 is the arrival time at 𝐼𝑘 . 𝑡𝑖→𝑗 (= 𝑡𝑗 − 𝑡𝑖 ) is the elapsed time along the path from 𝐼𝑖 to 𝐼𝑗 . When 𝐼𝑖 (𝑖 = 0, 1, ⋅ ⋅ ⋅ , 𝑛 − 1) receives the backward ant, 𝐼𝑖 updates the statistic 𝐷𝑖𝑗 (𝑗 = 𝑖 + 1, ⋅ ⋅ ⋅ , 𝑛) with sample mean 𝜇𝑖𝑗 and variance 𝜎𝑖𝑗 using 𝑡𝑖→𝑗 by exponential models [7]. 𝐼𝑖 also updates the pheromone trail 𝜏𝑖𝑛′ 𝑗 among 𝑃𝑖𝑗 as below:
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∑ 𝑖∈𝑉
⎛ ⎝𝑒𝑣 (𝑖) +
∑
⎞ 𝑒𝑙 (𝑙𝑖𝑗 )⎠.
(1)
𝑗∈𝑁𝑖
∑ ∑ min (⋅) = min(⋅) Since 𝑒𝑣 (𝑖) and 𝑒𝑙 (𝑙) ( are non-negative, ) ∑ holds. And, min 𝑒𝑣 (𝑖) + 𝑗∈𝑁𝑖 𝑒𝑙 (𝑙𝑖𝑗 ) is equivalent to maximize 𝐶(𝑖) by Corollary 1. Accordingly, the EMN problem in Eq. (1) can be re-defined as follow: ∑ (maximize 𝐶𝑘 (𝑖)) . (2) 𝑖∈𝑉
III. P ROPOSED A-ESR A LGORITHM The purpose of the A-ESR algorithm is to maximize 𝐶𝑘 (𝑖) (ie., to minimize the number of active links of node 𝑖); this goal is achieved by forcing the carried traffic on light-loaded links to be aggregated on other links, and then switching off the lighted-load links. For the purpose, A-ESR employs a single artificial ant colony on networks. Figure 1 illustrates the A-ESR logic in node 𝑖 for the employed ant colony. The logic is composed of the control plane (subsection A), which processes the individual artificial ants, and the data plane (subsection B), which processes the packets in an incoming flow. A. Control plane for artificial ants In the control plane, at regular intervals, a number of artificial forward ants asynchronously launch toward randomly chosen destination nodes. The forward ant explores a path and gathers (or measures) the status of all nodes along the explored path. The gathered information in the forward ant is transferred to the backward ant at the destination node; the backward ant moves backward to the source node while managing two important data structures of the explored nodes. Two important data structures, namely the delay statistic 𝐷𝑖𝑗 and the pheromone table 𝑃𝑖𝑗 , are illustrated in the right side of Figure 1. 𝐷𝑖𝑗 ∼ (𝜇𝑖𝑗 , 𝜎𝑖𝑗 ) is the statistic information about the elapsed time from node 𝑖 to node 𝑗 of a number of backward ants; 𝜇𝑖𝑗 and 𝜎𝑖𝑗 are the sample mean and variance estimated over the measured elapsed time, respectively. 𝑃𝑖𝑗 is the set of pheromone trails 𝜏𝑖𝑛′ 𝑗 (𝑛′ ∈ 𝑁𝑖 ); 𝜏𝑖𝑛′ 𝑗 indicates the learned desirability that the ant at current node 𝑖 intends to go through neighbor 𝑛′ toward node 𝑗. These data structures are updated in real-time whenever the backward ant arrives. Let’s assume the measured information by the ant to be {𝐼𝑘 , 𝑡𝑘 , 𝑘 = 0, 1, ⋅ ⋅ ⋅ , 𝑛}, where 𝐼𝑘 is the 𝑘-th intermediate
𝐼𝑖𝑛𝑓𝑖𝑗 , 𝑡𝑖→𝑗
(3)
where 𝜍 weights the number of most recent samples that affect the average value of the pheromone trails, 𝐼𝑖𝑛𝑓𝑖𝑗 = 𝜇𝑖𝑗 − √ 𝑧 (𝜎𝑖𝑗 / 𝑤), ( 𝑤 √ is the)number of required samples to estimate 𝐷𝑖𝑗 , 𝑧 = 1/ 1 − 𝑣 , and 𝑣 is the selected confidence level. Remark: As 𝑡𝑖→𝑗 measured by the artificial ant is close to 𝐼𝑖𝑛𝑓𝑖𝑗 , the pheromone trail is more accumulated. The pheromone trail represents the information about the current explored path, and is accumulated whenever backward ants arrive. That is, the accumulated pheromone trails include not only the previous information measured by previous ants, but also the instantaneous information measured by the current ant. Accordingly, this accumulated pheromone trails help the A-ESR algorithm promptly learn better routes more exactly. B. Data plane for incoming flows Suppose that an incoming flow 𝐹𝑠→𝑑 from source 𝑠 to destination 𝑑 arrives at node 𝑖. The packet processing engine in the data plane determines a neighbor node for packets in 𝐹𝑠→𝑑 . Let’s assume that 𝜏𝑖𝑛′ 𝑑 is the highest pheromone trail among 𝑃𝑖𝑑 . Corollary 2 sheds light on the property of 𝜏𝑖𝑛′ 𝑑 . Corollary 2. If 𝐹𝑠→𝑑 is routed through the neighbor 𝑛′ by 𝜏𝑖𝑛′ 𝑑 , then the delay from node 𝑖 to node 𝑑 of packets belonging to 𝐹𝑠→𝑑 is estimated not to be greater than 𝜇𝑖𝑑 . Proof: The highest pheromone trail 𝜏𝑖𝑛′ 𝑑 implicitly means that the paths taken by some artificial ants which pass through the neighbor 𝑛′ of node 𝑖 toward destination 𝑑 have delays that are close to 𝐼𝑖𝑛𝑓𝑖𝑑 , as seen in Eq. (3). Because the path of 𝐹𝑠→𝑑 taken by referring to 𝜏𝑖𝑛′ 𝑑 is one of paths taken by these ants, the delay of√𝐹𝑠→𝑑 is also estimated to be close to 𝐼𝑖𝑛𝑓𝑖𝑑 (= 𝜇𝑖𝑑 − 𝑧 (𝜎𝑖𝑑 / 𝑤) ≤ 𝜇𝑖𝑑 ). When receiving 𝐹𝑠→𝑑 , by considering the properties of the traffic centrality and the pheromone trails, node 𝑖 calculates the probability, which determines how greatly the energy consumption of node 𝑖 can be reduced while considering the network delay performance, for choosing neighbor 𝑛′ as: 𝑝𝑖𝑑 𝑛′ = 𝛽 ∑
𝑡𝑖𝑛′ 𝑗∈𝑁𝑖 𝑡𝑖𝑗
+ (1 − 𝛽) ∑
𝜏𝑖𝑛′ 𝑑 , 𝑗∈𝑁𝑖 𝜏𝑖𝑗𝑑
(4)
where 𝛽 is the factor to weight the traffic centrality. 𝐹𝑠→𝑑 is then routed to the neighbor with the highest probability. In this manner, 𝐹𝑠→𝑑 is transmitted until it reaches to destination. Theorem 1. If 𝛽 is properly chosen1 and incoming flows are routed by Eq. (4), the energy consumption of a node can be minimized while considering the network delay performance. 𝑖𝑑 Proof: Let’s assume that 𝑝𝑖𝑑 𝑛′ = max 𝑝𝑗 (𝑗 ∈ 𝑁𝑖 ) holds, and hence incoming flows are routed to neighbor 𝑛′ by 𝑝𝑖𝑑 𝑛′ . 1 As the weight factor 𝛽 → 0, the node tries to sustain the network delay performance, otherwise, reduce the energy consumption of network elements.
KIM et al.: ANT COLONY OPTIMIZATION BASED ENERGY SAVING ROUTING FOR ENERGY-EFFICIENT NETWORKS
Fig. 2.
Energy efficiency with respect to different algorithms.
Fig. 3.
Energy efficiency of A-ESR with respect to the weight factor 𝛽.
As more incoming flows are routed to neighbor 𝑛′ , 𝑡𝑖𝑛′ on link 𝑙𝑖𝑛′ in Eq. (4) more increases. As time passes, if 𝛽 is properly chosen, most of incoming flows are routed to neighbor 𝑛′ because 𝑝𝑖𝑑 𝑛′ radically increases. Eventually, ′ 𝑡∑ 𝑖𝑗 (𝑗 ∈ 𝑁𝑖 , 𝑗 ∕= 𝑛 ) ≈ 0 holds, and accordingly 𝑡𝑖𝑛′ ≈ 𝑗∈𝑁𝑖 𝑡𝑖𝑗 also holds, that is, max 𝐶(𝑖) (Corollary 1). Note that the second term in Eq. (4) indicates how closely the path taken by 𝜏𝑖𝑛′ is related to 𝐼𝑖𝑛𝑓𝑖𝑑 (Corollary 2). Accordingly, if 𝛽 is properly chosen, by Corollary 1 and 2, the A-ESR algorithm in node 𝑖 autonomously aggregates (or concentrates) the traffic on light-loaded links into some other links (i.e. solve the EMN problem) while considering the network delay performance. The energy consumption of network elements can be then reduced by switching off links 𝑙𝑖𝑗 (𝑗 ∈ 𝑁𝑖 , 𝑗 ∕= 𝑛′ ). IV. P ERFORMANCE E VALUATION AND D ISCUSSIONS We evaluate the A-ESR algorithm using the NS-2 simulator under the well-known 14-node NSFNet and the topologies provided by [8]. Especially, we refer to “Exodus,” composed of 79 nodes and 294 unidirectional links, “Ebone,” composed of 87 nodes and 322 links, and “Tiscali,” composed of 161 nodes and 656 links, networks; the characteristics of these topologies are explained in detail in [8]. The launching rate of the artificial ant was set to be 0.1 sec. Simulation scenarios are: during a simulation time, we generate tens of thousand flows; source and destination node of each flow are randomly chosen; the inter-arrival, holding time and the rate of the flow are exponentially distributed. We consider the energy efficiency 𝜂 which is defined by: ∑ 𝑡𝑜𝑓 𝑓𝑙 , 𝜂= 𝑡𝑜𝑛𝑙 + 𝑡𝑜𝑓 𝑓𝑙 𝑙∈𝐿
where 𝑡𝑜𝑓 𝑓𝑙 and 𝑡𝑜𝑛𝑙 are the total amount of time the link 𝑙 is switched off and switched on, respectively, and 𝐿 is the set of links in the given network topology.
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Figure 2 illustrates the energy efficiency under various network topologies with respect to OSPF, GreenOSPF [5], and A-ESR. In particular, in case of the GreenOSPF algorithm, the number of Exporter Router (𝐸𝑟) accounts for 5% ∼ 10% of total nodes. Simulation result shows that the A-ESR algorithm, taken as a whole, exhibits higher energy efficiency than other algorithms under real network topologies. It originates from the fact that the A-ESR algorithm gathers the on-line information about current network status by utilizing a number of artificial ants in real-time, and all incoming flows autonomously are aggregated under the network environments to be best-fitted for gathered current networks. Accordingly, the A-ESR algorithm can more efficiently aggregate the flows. The A-ESR algorithm adjusts the energy efficiency by controlling the weight factor 𝛽. In Figure 3 the energy efficiency of networks as a function of 𝛽 is depicted. As expected, increasing 𝛽 leads to increasing the energy efficiency. The reason is clear: when 𝛽 increases, the A-ESR algorithm considers the traffic centrality more important than the pheromone trails (that is, routing heavily depends on the traffic centrality), so flows are more aggregated on the heavyloaded links than the light-loaded links. When 𝛽 is equal to one, flows are aggregated on only one heavy-loaded link, so the energy consumption can be dramatically reduced by switching off all other links excepts the heavy-loaded link of a node. Simulation result shows that the A-ESR algorithm with 𝛽 = 1.0 (not shown) can reduce the energy consumption up to near 70%. However, it causes degradation of the network delay performance, accordingly the quality of services may not be acceptable for users. Accordingly, the value of 𝛽 should be carefully chosen as follows. It may be desirable for day hours, when delaysensitive services are prevailed, to decrease 𝛽. On the other hand, the larger value of 𝛽 may be required for night hours when delay tolerable services such as FTP are prevailed. V. C ONCLUSIONS In this letter, we provided an ACO based energy saving routing which dramatically reduces the energy consumption by making use of the pheromone trails. Simulation results show that the proposed A-ESR algorithm can get better performance than previous works. For future work, extension of A-ESR to dynamically allocate the 𝛽 value with respect to the delay requirement of the incoming flow remains. R EFERENCES [1] Draft deliverable on “Overview of energy saving of networks,” ITU-T FGFN-OD65, Oct. 2010. [2] M. Gupta and S. Singh, “Using low-power modes for energy conservation in Ethernet LANs,” IEEE INFOCOM, May 2007. [3] M. Andrews et al., “Routing for energy minimization in the speed scaling model,” IEEE INFOCOM, Mar. 2010. [4] L. Chiaraviglio et al., “Reducing power consumption in backbone networks,” IEEE ICC, June 2009. [5] A. Cianfrani et al., “An energy saving routing algorithm for a Green OSPF protocol,” IEEE INFOCOMW, Mar. 2010. [6] F. Dressler and O. B. Akan, “Bio-inspired networking: from theory to practice,” IEEE Commun. Mag., vol. 48, no. 11, Nov. 2010. [7] M. Dorigo and T. Stutzle, Ant Colony Optimization. The MIT Press, 2004. [8] N. Spring et al., “Measuring ISP topologies with Rocketfuel,” ACM SIGCOMM, Aug. 2002.
